% LAD definitions
\def\vx{{\vec x}}
\def\vxdot{{\dot\vx}} \def\vxddot{{\ddot\vx}}
\def\tpose{^\top}
\def\ru{{\rm u}}
\def\vc{{\vec c}}
\def\vrho{{{\bf p}}}
\def\mat#1{{\bf#1}}
\def\vec#1{{\bf#1}}
\def\bold#1{\setbox0=\hbox{#1}
 \kern-.025em\copy0\kern-\wd0
 \kern.05em\copy0\kern-\wd0
 \kern-.025em\raise.0433em\box0}
\def\vsigma{{\bf \sigma}}
\def\vepsilon{{\bf \epsilon}}
\def\ssqueeze{\vspace{-0.5cm}}

\def\bsqueeze{\vspace*{-0.8cm}}
\def\bpsqueeze{\vspace*{-0.6cm}}
\def\asqueeze{\vspace{-0.5cm}}


\def\inv{^{-1}}
\def\vuhat{{\hat \vec u}}
\def\avtk{{t_{k}}}
\def\bvtk{{t_{k+1}}}
\def\vu{{\vec u}}
\def\vuhat{{\hat \vec u}}
\def\vq{{\vec q}}
\def\vqdot{{\dot\vq}}
\def\tpose{^\top}
\def\mat#1{{\bf#1}}
\def\extvec#1#2#3{{~^{#1}{\bf#2}_{#3}}}
\def\extvecrm#1#2#3{{~^{{\rm #1}}{\bf#2}_{#3}}}

\def\cavindex{{\cal V\cal I}}
\def\caawpoint{{\extvec{\Phi}{x}{j}}}
\def\caaipointrm{{\extvecrm{I}{x}{j}}}
\def\caaipoint{{\extvec{I}{x}{j}}}

\newcounter{lfigcounter}
\newenvironment{IonTab}{\begin{table}[htb]}{\end{table}}
\newenvironment{IonFig}{\setcounter{lfigcounter}{1}\begin{figure}}{\end{figure}}
\newenvironment{IonFigH}{\setcounter{lfigcounter}{1}\begin{figure}[h]}{\end{figure}}
\newenvironment{IonFigT}{\setcounter{lfigcounter}{1}\begin{figure}[t]}{\end{figure}}
\def\ionbox#1{\makebox[#1]{(\alph{lfigcounter})}\stepcounter{lfigcounter}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
